Oxidative stress and inflammation are two conditions that coexist in many multifactorial diseases such as atherosclerosis and neurodegeneration. Thus, the design of multifunctional compounds that can concurrently tackle two or more therapeutic targets is an appealing approach. In this study, the basic NSAID structure was fused with the antioxidant moieties 3,5-di-tert-butyl-4-hydroxybenzoic acid (BHB), its reduced alcohol 3,5-di-tert-butyl- 4-hydroxybenzyl alcohol (BHBA), or 6-hydroxy-2,5,7,8-tetramethylchromane-2-carboxylic acid (Trolox), a hydrophilic analogue of α-tocopherol. Machine learning algorithms were utilized to validate the potential dual effect (anti-inflammatory and antioxidant) of the designed analogues. Derivatives 1–17 were synthesized by known esterification methods, with good to excellent yields, and were pharmacologically evaluated both in vitro and in vivo for their antioxidant and anti-inflammatory activity, whereas selected compounds were also tested in an in vivo hyperlipidemia protocol. Furthermore, the activity/binding affinity of the new compounds for lipoxygenase-3 (LOX-3) was studied not only in vitro but also via molecular docking simulations. Experimental results demonstrated that the antioxidant and anti-inflammatory activities of the new fused molecules were increased compared to the parent molecules, while molecular docking simulations validated the improved activity and revealed the binding mode of the most potent inhibitors. The purpose of their design was justified by providing a potentially safer and more efficient therapeutic approach for multifactorial diseases.